11 citations · 115 across the 90 of their papers we have counts for
8 papers · 1 filter
A combinatorial identity with application to Catalan numbers
Hao Pan, Zhi-Wei Sun
By a very simple argument, we prove that if are nonnegative integers then $$\sum_{k=0}^l(-1)^{m-k}\binom{l}{k}\binom{m-k}{n}\binom{2k}{k-2l+m} =\sum_{k=0}^l\binom{l}{k}\bin…
Arithmetic properties of q-Fibonacci numbers and q-Pell numbers
Hao Pan
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.
A congruence involving products of -binomial coefficients
Hao Pan, Hui-Qin Cao
In this paper we establish a -analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.
A q-analogue of Lehmer's congruence
Hao Pan
We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.
A q-analogue of Wolstenholme's harmonic series congruence
Ling-Ling Shi, Hao Pan
We establish a q-analogue of Wolstenholme's harmonic series congruence.
On q-Euler numbers, q-Salie numbers and q-Carlitz numbers
Hao Pan, Zhi-Wei Sun
Let for n=0,1,2,.... Define q-Euler numbers , q-Salié numbers and q-Carlitz numbers as follows: $$\sum_{n=0}^{\infty}E_…